Inter-isotope determination of ultracold rubidium interactions from three high-precision experiments

Combining the measured binding energies of four of the most weakly bound rovibrational levels of the $^{87}$Rb$_2$ molecule with the results of two other recent high-precision rubidium experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of $^{85}$Rb and $^{87}$Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. Using the consistent picture of the interactions that thus arises we are led to predictions for scattering lengths, clock shifts, Feshbach resonance fields and widths with an unprecedented level of accuracy. To demonstrate this, we predict two Feshbach resonances in mixed-spin scattering channels at easily accessible magnetic field strengths, which we expect to play a role in the damping of coherent spin oscillations.